1  /* Double-precision vector (Advanced SIMD) log function.
       2  
       3     Copyright (C) 2023 Free Software Foundation, Inc.
       4     This file is part of the GNU C Library.
       5  
       6     The GNU C Library is free software; you can redistribute it and/or
       7     modify it under the terms of the GNU Lesser General Public
       8     License as published by the Free Software Foundation; either
       9     version 2.1 of the License, or (at your option) any later version.
      10  
      11     The GNU C Library is distributed in the hope that it will be useful,
      12     but WITHOUT ANY WARRANTY; without even the implied warranty of
      13     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
      14     Lesser General Public License for more details.
      15  
      16     You should have received a copy of the GNU Lesser General Public
      17     License along with the GNU C Library; if not, see
      18     <https://www.gnu.org/licenses/>.  */
      19  
      20  #include "v_math.h"
      21  
      22  static const struct data
      23  {
      24    float64x2_t poly[5];
      25    float64x2_t ln2;
      26    uint64x2_t min_norm, special_bound, sign_exp_mask;
      27  } data = {
      28    /* Worst-case error: 1.17 + 0.5 ulp.
      29       Rel error: 0x1.6272e588p-56 in [ -0x1.fc1p-9 0x1.009p-8 ].  */
      30    .poly = { V2 (-0x1.ffffffffffff7p-2), V2 (0x1.55555555170d4p-2),
      31  	    V2 (-0x1.0000000399c27p-2), V2 (0x1.999b2e90e94cap-3),
      32  	    V2 (-0x1.554e550bd501ep-3) },
      33    .ln2 = V2 (0x1.62e42fefa39efp-1),
      34    .min_norm = V2 (0x0010000000000000),
      35    .special_bound = V2 (0x7fe0000000000000), /* asuint64(inf) - min_norm.  */
      36    .sign_exp_mask = V2 (0xfff0000000000000)
      37  };
      38  
      39  #define A(i) d->poly[i]
      40  #define N (1 << V_LOG_TABLE_BITS)
      41  #define IndexMask (N - 1)
      42  #define Off v_u64 (0x3fe6900900000000)
      43  
      44  struct entry
      45  {
      46    float64x2_t invc;
      47    float64x2_t logc;
      48  };
      49  
      50  static inline struct entry
      51  lookup (uint64x2_t i)
      52  {
      53    /* Since N is a power of 2, n % N = n & (N - 1).  */
      54    struct entry e;
      55    e.invc[0] = __v_log_data.invc[i[0] & IndexMask];
      56    e.logc[0] = __v_log_data.logc[i[0] & IndexMask];
      57    e.invc[1] = __v_log_data.invc[i[1] & IndexMask];
      58    e.logc[1] = __v_log_data.logc[i[1] & IndexMask];
      59    return e;
      60  }
      61  
      62  static float64x2_t VPCS_ATTR NOINLINE
      63  special_case (float64x2_t x, float64x2_t y, uint64x2_t cmp)
      64  {
      65    return v_call_f64 (log, x, y, cmp);
      66  }
      67  
      68  float64x2_t VPCS_ATTR V_NAME_D1 (log) (float64x2_t x)
      69  {
      70    const struct data *d = ptr_barrier (&data);
      71    float64x2_t z, r, r2, p, y, kd, hi;
      72    uint64x2_t ix, iz, tmp, cmp;
      73    int64x2_t k;
      74    struct entry e;
      75  
      76    ix = vreinterpretq_u64_f64 (x);
      77    cmp = vcgeq_u64 (vsubq_u64 (ix, d->min_norm), d->special_bound);
      78  
      79    /* x = 2^k z; where z is in range [Off,2*Off) and exact.
      80       The range is split into N subintervals.
      81       The ith subinterval contains z and c is near its center.  */
      82    tmp = vsubq_u64 (ix, Off);
      83    k = vshrq_n_s64 (vreinterpretq_s64_u64 (tmp), 52); /* arithmetic shift.  */
      84    iz = vsubq_u64 (ix, vandq_u64 (tmp, d->sign_exp_mask));
      85    z = vreinterpretq_f64_u64 (iz);
      86    e = lookup (vshrq_n_u64 (tmp, 52 - V_LOG_TABLE_BITS));
      87  
      88    /* log(x) = log1p(z/c-1) + log(c) + k*Ln2.  */
      89    r = vfmaq_f64 (v_f64 (-1.0), z, e.invc);
      90    kd = vcvtq_f64_s64 (k);
      91  
      92    /* hi = r + log(c) + k*Ln2.  */
      93    hi = vfmaq_f64 (vaddq_f64 (e.logc, r), kd, d->ln2);
      94    /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi.  */
      95    r2 = vmulq_f64 (r, r);
      96    y = vfmaq_f64 (A (2), A (3), r);
      97    p = vfmaq_f64 (A (0), A (1), r);
      98    y = vfmaq_f64 (y, A (4), r2);
      99    y = vfmaq_f64 (p, y, r2);
     100    y = vfmaq_f64 (hi, y, r2);
     101  
     102    if (__glibc_unlikely (v_any_u64 (cmp)))
     103      return special_case (x, y, cmp);
     104    return y;
     105  }